Document No. :: IITK-GSDMA-EQ21-V2.0 Final Report :: A - Earthquake Codes IITK-GSDMA Project on Building Codes Explanatory Examples on Indian Seismic Code IS 1893 (Part I) by Dr. Sudhir K Jain Department of Civil Engineering Indian Institute of Technology Kanpur Kanpur • The solved examples included in this document are based on a draft code being developed under IITK-GSDMA Project on Building Codes. The draft code is available at http://www.nicee.org/IITK-GSDMA/IITKGSDMA.htm (document number IITK-GSDMA-EQ05-V3.0). • This document has been developed through the IITK-GSDMA Project on Building Codes. • The views and opinions expressed are those of the authors and not necessarily of the GSDMA, the World Bank, IIT Kanpur, or the Bureau of Indian Standards. • Comments and feedbacks may please be forwarded to: Prof. Sudhir K Jain, Dept. of Civil Engineering, IIT Kanpur, Kanpur 208016, email: [email protected] Examples on IS 1893(Part 1) CONTENTS Sl. No 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Title Calculation of Design Seismic Force by Static Analysis Method Calculation of Design Seismic Force by Dynamic Analysis Method Location of Centre of Mass Location of Centre of Stiffness Lateral Force Distribution as per Torsion Provisions of IS 1893-2002 (Part I) Lateral Force Distribution as per New Torsion Provisions Design for Anchorage of an Equipment Anchorage Design for an Equipment Supported on Vibration Isolator Design of a Large Sign Board on a Building Liquefaction Analysis Using SPT Data Liquefaction Analysis Using CPT Data IITK-GSDMA-EQ21-V2.0 Page No. 4 7 10 11 12 14 16 18 20 21 23 Examples on IS 1893(Part 1) Example 1 – Calculation of Design Seismic Force by Static Analysis Method Problem Statement: Consider a four-storey reinforced concrete office building shown in Fig. 1.1. The building is located in Shillong (seismic zone V). The soil conditions are medium stiff and the entire building is supported on a raft foundation. The R. C. frames are infilled with brick-masonry. The lumped weight due to dead loads is 12 kN/m2 on floors and 10 kN/m2 on the roof. The floors are to cater for a live load of 4 kN/m2 on floors and 1.5 kN/m2 on the roof. Determine design seismic load on the structure as per new code. [Problem adopted from Jain S.K, “A Proposed Draft for IS:1893 Provisions on Seismic Design of Buildings; Part II: Commentary and Examples”, Journal of Structural Engineering, Vol.22, No.2, July 1995, pp.73-90 ] y (1) (2) (3) (4) (4) (5) (A) 3 @ 5000 (B) (C) (D) x 4 @ 5000 PLAN 3200 3200 3200 4200 ELEVATION Figure 1.1 – Building configuration IITK-GSDMA-EQ21-V2.0 Example 1/Page 4 Examples on IS 1893(Part 1) = 0.09(13.8) / 20 = 0.28 sec The building is located on Type II (medium soil). Solution: Design Parameters: For seismic zone V, the zone factor Z is 0.36 (Table 2 of IS: 1893). Being an office building, the importance factor, I, is 1.0 (Table 6 of IS: 1893). Building is required to be provided with moment resisting frames detailed as per IS: 13920-1993. Hence, the response reduction factor, R, is 5. (Table 7 of IS: 1893 Part 1) Seismic Weights: The floor area is 15×20=300 sq. m. Since the live load class is 4kN/sq.m, only 50% of the live load is lumped at the floors. At roof, no live load is to be lumped. Hence, the total seismic weight on the floors and the roof is: Floors: W1=W2 =W3 =300×(12+0.5×4) = 4,200 kN Roof: = 300×10 = 3,000 kN W4 (clause7.3.1, Table 8 of IS: 1893 Part 1) Total Seismic weight of the structure, W = ΣW i = 3×4,200 + 3,000 = 15,600 kN Fundamental Period: Lateral load resistance is provided by moment resisting frames infilled with brick masonry panels. Hence, approximate fundamental natural period: (Clause 7.6.2. of IS: 1893 Part 1) From Fig. 2 of IS: 1893, for T=0.28 sec, S a g = 2.5 ZI S a = Ah 2R g 0.36 × 1.0 × 2.5 = 2×5 = 0.09 (Clause 6.4.2 of IS: 1893 Part 1) Design base shear VB = AhW = 0.09 × 15,600 = 1,440 kN (Clause 7.5.3 of IS: 1893 Part 1) Force Distribution with Building Height: The design base shear is to be distributed with height as per clause 7.7.1. Table 1.1 gives the calculations. Fig. 1.2(a) shows the design seismic force in X-direction for the entire building. EL in Y-Direction: T = 0.09 h d = 0.09(13.8) / 15 = 0.32 sec Sa g Ah = 2.5; = 0.09 Therefore, for this building the design seismic force in Y-direction is same as that in the Xdirection. Fig. 1.2(b) shows the design seismic force on the building in the Y-direction. EL in X-Direction: T = 0.09h / d IITK-GSDMA-EQ21-V2.0 Example 1/Page 5 Examples on IS 1893(Part 1) Table 1.1 – Lateral Load Distribution with Height by the Static Method Storey Level Wi (kN ) hi (m) Wi hi2 × (1000) Wi hi2 ∑W h 2 i i Lateral Force at Level for EL direction (kN) X 4 3 2 1 Σ 3,000 4,200 4,200 4,200 13.8 10.6 7.4 4.2 571.3 471.9 230.0 74.1 1,347.3 0.424 0.350 0.171 0.055 1,000 611 504 246 79 1,440 ith in Y 611 504 246 79 1,440 Figure 1.2 -- Design seismic force on the building for (a) X-direction, and (b) Y-direction. IITK-GSDMA-EQ21-V2.0 Example 1/Page 6 Examples on IS 1893(Part 1) Example 2 – Calculation of Design Seismic Force by Dynamic Analysis Method Problem Statement: For the building of Example 1, the dynamic properties (natural periods, and mode shapes) for vibration in the X-direction have been obtained by carrying out a free vibration analysis (Table 2.1). Obtain the design seismic force in the X-direction by the dynamic analysis method outlined in cl. 7.8.4.5 and distribute it with building height. Table 2.1 – Free Vibration Properties of the building for vibration in the X-Direction Natural Period (sec) Roof 3rd Floor 2nd Floor 1st Floor Mode 1 0.860 Mode Shape 1.000 0.904 0.716 0.441 Mode 2 0.265 Mode 3 0.145 1.000 0.216 -0.701 -0.921 1.000 -0.831 -0.574 1.016 [Problem adopted from, Jain S.K, “A Proposed Draft for IS: 1893 Provisions on Seismic Design of Buildings; Part II: Commentary and Examples”, Journal of Structural Engineering, Vol.22, No.2, July 1995, pp.73-90] Solution: Table 2.2 -- Calculation of modal mass and modal participation factor (clause 7.8.4.5) Storey Level i Weight Wi (kN ) 4 3 2 1 3,000 4,200 4,200 4,200 15,600 Σ [∑ w φ ] = 2 Mk i g ik ∑w φ i 2 ik % of Total weight Pk = ∑w φ ∑w φ i i ik 2 ik Mode 1 1.000 0.904 0.716 0.441 3,000 3,797 3,007 1,852 11,656 Mode 2 3,000 3,432 2,153 817 9,402 11,6562 14,450kN = 9,402 g g 1.000 0.216 -0.701 -0.921 3,000 907 -2,944 -3,868 -2,905 Mode 3 3,000 196 2,064 3,563 8,822 2,9052 957kN = 8,822 g g = 14,45,000 kg 1.000 -0.831 -0.574 1.016 3,000 -3,490 -2,411 4,267 1,366 1,3662 161kN = 11,620 g g =95,700 kg = 16,100 kg 92.6% 6.1% 1.0% 11,656 = 1.240 9,402 − 2,905 = −0.329 8,822 1,366 = 0.118 11,620 It is seen that the first mode excites 92.6% of the total mass. Hence, in this case, codal requirements on number of modes to be considered such that at least 90% of the total mass is excited, will be satisfied by considering the first mode of IITK-GSDMA-EQ21-V2.0 3,000 2,900 1,384 4,335 11,620 vibration only. However, for illustration, solution to this example considers the first three modes of vibration. The lateral load Qik acting at ith floor in the kth mode is Qik = Ahk φ ik Pk Wi Example 2/Page 7 Examples on IS 1893(Part 1) (clause 7.8.4.5 c of IS: 1893 Part 1) ZI (S a / g ) 2R 0.36 × 1 = × (2.5) 2×5 = 0.09 = 0.09 × (−0.329) × φi 2 × Wi = Ah 2 The value of Ahk for different modes is obtained from clause 6.4.2. Mode 1: T1 = 0.860 sec; 1 .0 (S a / g ) = = 1.16 ; 0.86 ZI Ah1 = (S a / g ) 2R 0.36 × 1 = × (1.16) 2×5 = 0.0418 Qi1 = 0.0418 × 1.240 × φ i1 × Wi Qi1 Mode 3: T3 = 0.145 sec; ( S a / g ) = 2.5 ; ZI Ah 3 = (S a / g ) 2R 0.36 × 1 = × (2.5) 2×5 = 0.09 Qi 3 = 0.09 × (0.118) × φ i 3 × Wi Mode 2: T2 = 0.265 sec; ( S a / g ) = 2.5 ; Table 2.3 summarizes the calculation of lateral load at different floors in each mode. Table 2.3 – Lateral load calculation by modal analysis method (earthquake in X-direction) Weight Wi Floor Level i 4 3 2 1 (kN ) 3,000 4,200 4,200 4,200 Mode 1 φ i1 Q i1 1.000 0.904 0.716 0.441 155.5 196.8 155.9 96.0 Mode 2 V i1 155.5 352.3 508.2 604.2 Since all of the modes are well separated (clause 3.2), the contribution of different modes is combined by the SRSS (square root of the sum of the square) method V4 = [(155.5)2+ (88.8)2+ (31.9)2]1/2 = 182 kN V3 = [(352.3)2+ (115.6)2+ (5.2)2]1/2 = 371 kN V2 = [(508.2)2+ (28.4)2+ (30.8)2]1/2 = 510 kN 2 2 2 1/2 V1 = [(604.2) + (86.2) + (14.6) ] = 610 kN (Clause 7.8.4.4a of IS: 1893 Part 1) The externally applied design loads are then obtained as: Q4 = V4 = 182 kN Q3 = V3 – V4 = 371 – 182 = 189 kN Q2 = V2 – V3 = 510 – 371 = 139 kN Q1 = V1 – V2 = 610 – 510 = 100 kN (Clause 7.8.4.5f of IS: 1893 Part 1) IITK-GSDMA-EQ21-V2.0 φ i2 Q i2 1.000 -88.8 0.216 -26.8 -0.701 87.2 -0.921 114.6 Mode 3 V i2 φ i3 -88.8 -115.6 -28.4 86.2 1.000 -0.831 -0.574 1.016 Q i3 V i3 31.9 -37.1 -25.6 45.4 31.9 -5.2 -30.8 14.6 Clause 7.8.2 requires that the base shear obtained by dynamic analysis (VB = 610 kN) be compared with that obtained from empirical fundamental period as per Clause 7.6. If VB is less than that from empirical value, the response quantities are to be scaled up. We may interpret “base shear calculated using a fundamental period as per 7.6” in two ways: 1. We calculate base shear as per Cl. 7.5.3. This was done in the previous example for the same building and we found the base shear as 1,404 kN. Now, dynamic analysis gives us base shear of 610 kN which is lower. Hence, all the response quantities are to be scaled up in the ratio (1,404/610 = 2.30). Thus, the seismic forces obtained above by dynamic analysis should be scaled up as follows: Q4 = 182 × 2.30 = 419 kN Q3 = 189 × 2.30 = 435 kN Q2 = 139 × 2.30 = 320 kN Example 2/Page 8 Examples on IS 1893(Part 1) Q1 = 100 × 2.30 = 230 kN = 1,303 kN 2. We may also interpret this clause to mean that we redo the dynamic analysis but replace the fundamental time period value by Ta (= 0.28 sec). In that case, for mode 1: T1 = 0.28 sec; ( S a / g ) = 2.5 ; Q4 = 182 Q3 = 189 Q2 = 139 Q1 = 100 ZI (S a / g ) 2R =0.09 Modal mass times Ah1 = 14,450 × 0.09 = 1,300 kN Ah1 Notice that most of the base shear is contributed by first mode only. In this interpretation of Cl 7.8.2, we need to scale up the values of response quantities in the ratio (1,303/610 = 2.14). For instance, the external seismic forces at floor levels will now be: = Base shear in modes 2 and 3 is as calculated earlier: Now, base shear in first mode of vibration =1300 kN, 86.2 kN and 14.6 kN, respectively. Total base shear by SRSS × × × × 2.14 = 389 kN 2.14 = 404 kN 2.14 = 297 kN 2.14 = 214 kN Clearly, the second interpretation gives about 10% lower forces. We could make either interpretation. Herein we will proceed with the values from the second interpretation and compare the design values with those obtained in Example 1 as per static analysis: 2 2 2 = 1300 + 86.2 + 14.6 Table 2.4 – Base shear at different storeys Floor Level i 4 Q (static) Q (dynamic, scaled) 611 kN 389 kN 611 kN 3 504 kN 404 kN 1,115kN 793 kN 5,386 kNm 2 297 kN 297 kN 1,412kN 1,090 kN 9.632 kNm 1 79 kN 214 kN 1,491 kN 1,304 kN 15,530 kNm Storey Shear V (static) Storey ShearV (dynamic, scaled) 389 kN Storey Moment, M (Static) 1,907 kNm Storey Moment, M (Dynamic) 1,245 kNm 3,782 kNm 7,270 kNm 12,750 kNm Notice that even though the base shear by the static and the dynamic analyses are comparable, there is considerable difference in the lateral load distribution with building height, and therein lies the advantage of dynamic analysis. For instance, the storey moments are significantly affected by change in load distribution. IITK-GSDMA-EQ21-V2.0 Example 2/Page 9 Examples on IS 1893(Part 1) Example 3 – Location of Centre of Mass Problem Statement: Locate centre of mass of a building having non-uniform distribution of mass as shown in the figure 3.1 10 m 4m 1200 kg/m2 1000 kg/m2 8m A 20 m Figure 3.1 –Plan Solution: Let us divide the roof slab into three rectangular parts as shown in figure 2.1 Y= (10 × 4 × 1200) × 6 + (10 × 4 × 1000) × 6 + (20 × 4 × 1000) × 2 (10 × 4 × 1200) + (10 × 4 × 1000) + (20 × 4 × 1000) = 4.1 m Hence, coordinates of centre of mass are (9.76, 4.1) 10 m I 4m II 1200 kg/m2 1000 kg/m2 III 8m 20 m Figure 3.2 Mass of part I is 1200 kg/m2, while that of the other two parts is 1000 kg/m2. . Let origin be at point A, and the coordinates of the centre of mass be at (X, Y) (10 × 4 × 1200) × 5 + (10 × 4 × 1000) × 15 + (20 × 4 × 1000) × 10 (10 × 4 × 1200) + (10 × 4 × 1000) + (20 × 4 × 1000) = 9.76 m X = IITK-GSDMA-EQ21 –V2.0 Example 3 /Page10 Examples on IS 1893(Part 1) Example 4 – Location of Centre of Stiffness Problem Statement: The plan of a simple one storey building is shown in figure 3.1. All columns and beams are same. Obtain its centre of stiffness. 5m 5m 5m 5m 10 m Figure 4.1 –Plan Solution: In the X-direction there are three identical frames located at uniform spacing. Hence, the ycoordinate of centre of stiffness is located symmetrically, i.e., at 5.0 m from the left bottom corner. In the Y-direction, there are four identical frames having equal lateral stiffness. However, the spacing is not uniform. Let the lateral stiffness of each transverse frame be k, and coordinating of center of stiffness be (X, Y). X = k × 0 + k × 5 + k × 10 + k × 20 = 8.75 m k+k+k+k Hence, coordinates of centre of stiffness are (8.75, 5.0). IITK-GSDMA-EQ21 –V2.0 Example 4 /Page11 Examples on IS 1893(Part 1) Example 5 –Lateral Force Distribution as per Torsion Provisions of IS 1893-2002 (Part 1) Problem Statement: Consider a simple one-storey building having two shear walls in each direction. It has some gravity columns that are not shown. All four walls are in M25 grade concrete, 200 thick and 4 m long. Storey height is 4.5 m. Floor consists of cast-in-situ reinforced concrete. Design shear force on the building is 100 kN in either direction. Compute design lateral forces on different shear walls using the torsion provisions of 2002 edition of IS 1893 (Part 1). Y 2m 4m 4m C 4m 8m B A X D 16m Figure 5.1 – Plan Solution: Grade of concrete: M25 E = 5000 25 = 25000 N/mm2 Storey height h = 4500 m Thickness of wall t = 200 mm Length of walls L = 4000 mm All walls are same, and hence, spaces have same lateral stiffness, k. Centre of mass (CM) will be the geometric centre of the floor slab, i.e., (8.0, 4.0). Centre of rigidity (CR) will be at (6.0, 4.0). EQ Force in X-direction: Because of symmetry in this direction, calculated eccentricity = 0.0 m Design eccentricity: ed = 1.5 × 0.0 + 0.05 × 8 = 0.4 , and IITK-GSDMA-EQ21 –V2.0 ed = 0.0 − 0.05 × 8 = −0.4 (Clause 7.9.2 of IS 1893:2002) Lateral forces in the walls due to translation: KC FCT = F = 50.0 kN KC + K D KD F = 50.0 kN FDT = KC + K D Lateral forces in the walls due to torsional moment: K i ri (Fed ) FiR = K i ri2 ∑ i = A , B ,C , D where ri is the distance of the shear wall from CR. All the walls have same stiffness, KA = KB = KC = KD = k, and rA = -6.0 m rB = -6.0 m Example 5 /Page 12 Examples on IS 1893(Part 1) rC = 4.0 m rD = -4.0 m, and ed = ±0.4 m FAR = rA k (Fed ) = 2 rA + rB2 + rC2 + rD2 k ( ( 2 B ) - 21.92 kN Therefore, FAR rA k (Fed ) = r + r + rC2 + rD2 k 2 A ) = ± 2.31 kN Similarly, FBR = ± 2.31 kN FCR = ± 1.54 kN FDR = ± 1.54 kN Total lateral forces in the walls due to seismic load in X direction: FA = 2.31 kN FB = 2.31 kN FC = Max (50 ± 1.54 ) = 51.54 kN FD = Max (50 ± 1.54 ) = 51.54 kN EQ Force in Y-direction: Calculated eccentricity= 2.0 m Design eccentricity: ed = 1.5 × 2.0 + 0.05 × 16 = 3.8 m or = 2.0 − 0.05 × 16 = 1.2 m Lateral forces in the walls due to translation: KA F = 50.0 kN KA + KB KB FBT = F = 50.0 kN KA + KB Lateral force in the walls due to torsional moment: when ed = 3.8 m FAT = IITK-GSDMA-EQ21-V2.0 Similarly, FBR = 21.92 kN FCR = -14.62 kN FDR = 14.62 kN Total lateral forces in the walls: FA = 50 - 21.92= 28.08 kN FB = 50 +20.77= 71.92 kN FC = -14.62 kN FD = 14.62 kN Similarly, when ed = 1.2 m, then the total lateral forces in the walls will be, FA = 50 – 6.93 = 43.07 kN FB = 50 + 6.93 = 56.93 kN FC = - 4.62 kN FD = 4.62 kN Maximum forces in walls due to seismic load in Y direction: FA = Max (28.08, 43.07) = 43.07 kN; FB = Max (71.92, 56.93) = 71.92 kN; FC = Max (14.62, 4.62) = 14.62 kN; FD = Max (14.62, 4.62) = 14.62 kN; Combining the forces obtained from seismic loading in X and Y directions: FA = 43.07 kN FB =71.92 kN FC =51.54 kN FD =51.54 kN. However, note that clause 7.9.1 also states that “However, negative torsional shear shall be neglected”. Hence, wall A should be designed for not less than 50 kN. Example 5/Page 13 Examples on IS 1893(Part 1) Example 6 – Lateral Force Distribution as per New Torsion Provisions Problem Statement: For the building of example 5, compute design lateral forces on different shear walls using the torsion provisions of revised draft code IS 1893 (part 1), i.e., IITK-GSDMA-EQ05-V2.0. Y 2m 4m 4m 6m C 4m 8m B A X D 16m Figure 6.1 – Plan Solution: Grade of concrete: M25 E = 5000 25 = 25000 N/mm2 Storey height h = 4500 m Thickness of wall t = 200 mm Length of walls L = 4000 mm All walls are same, and hence, same lateral stiffness, k. Centre of mass (CM) will be the geometric centre of the floor slab, i.e., (8.0, 4.0). Centre of rigidity (CR) will be at (6.0, 4.0). EQ Force in X-direction: Because of symmetry in this direction, calculated eccentricity = 0.0 m Design eccentricity, ed = 0.0 ± 0.1 × 8 = ±0.8 (clause 7.9.2 of Draft IS 1893: (Part1)) Lateral forces in the walls due to translation: KC F = 50.0 kN FCT = KC + K D KD FDT = F = 50.0 kN KC + K D Lateral forces in the walls due to torsional moment: IITK-GSDMA-EQ21 –V2.0 FiR = K i ri (Fed ) ∑ K i ri 2 i = A , B ,C , D where ri is the distance of the shear wall from CR All the walls have same stiffness, KA = KB = KC = KD = k rA= -6.0 m rB= -6.0 m rC= 4.0 m rD= -4.0 m FAR = rA k (Fed ) r + r + rC2 + rD2 k ( 2 A ) 2 B = - 4.62 kN Similarly, FBR = 4.62 kN FCR = 3.08 kN FDR = -3.08 kN Total lateral forces in the walls: FA = 4.62 kN FB = - 4.62 kN FC = 50+3.08 = 53.08 kN FD = 50-3.08 = 46.92 kN Example 6 /Page 14 Examples on IS 1893(Part 1) Similarly, when ed= - 0.8 m, then the lateral forces in the walls will be, FA = - 4.62 kN FB = 4.62 kN FC = 50-3.08 = 46.92 kN FD = 50+3.08 = 53.08kN Similarly, FBR = 20.77 kN FCR = 13.85 kN FDR = -13.8 kN Total lateral forces in the walls: FA = 50-20.77= 29.23 kN FB = 50+20.77= 70.77 kN FC = 13.85 kN FD = -13.85 kN Design lateral forces in walls C and D are: FC= FD= 53.05 kN EQ Force in Y-direction: Calculated eccentricity= 2.0 m Design eccentricity, ed = 2.0 + 0.1 × 16 = 3.6 m or ed = 2.0 − 0.1 × 16 = 0.4 m Similarly, when ed= 0.4 m, then the total lateral forces in the walls will be, FA = 50-2.31= 47.69 kN FB = 50+2.31= 53.31 kN FC = 1.54 kN FD = - 1.54 kN Lateral forces in the walls due to translation: Maximum forces in walls A and B FA =47.69 kN, FB =70.77 kN KA F = 50.0 kN KA + KB KB F = 50.0 kN FBT = KA + KB Lateral force in the walls due to torsional moment: when ed= 3.6 m FAT = FAR = rA k (Fed ) = r + r + rC2 + rD2 k ( 2 A 2 B ) Design lateral forces in all the walls are as follows: FA =47.69 kN FB =70.77 kN FC =53.05 kN FD =53.05 kN. - 20.77 kN IITK-GSDMA-EQ21-V2.0 Example 6/Page 15 Examples on IS 1893(Part 1) Example 7 – Design for Anchorage of an Equipment Problem Statement: A 100 kN equipment (Figure 7.1) is to be installed on the roof of a five storey building in Simla (seismic zone IV). It is attached by four anchored bolts, one at each corner of the equipment, embedded in a concrete slab. Floor to floor height of the building is 3.0 m. except the ground storey which is 4.2 m. Determine the shear and tension demands on the anchored bolts during earthquake shaking. Wp Fp CG 1.5 m Anchor bolt Anchor 1.0 m bolt Figure 7.1– Equipment installed at roof Solution: Zone factor, Z = 0.24 (for zone IV, Table 2 of IS 1893), Height of point of attachment of the equipment above the foundation of the building, x = (4.2 +3.0 × 4) m = 16.2 m, The design seismic force Z ⎛ x⎞ a Fp = ⎜1 + ⎟ p I pW p 2 ⎝ h ⎠ Rp Height of the building, h = 16.2 m, Amplification factor of the equipment, a p = 1 (rigid component, Table 11), = Response modification factor Rp = 2.5 (Table 11), = 9.6 kN < 0.1W p = 10.0kN Importance factor Ip = 1 (not life safety component, Table 12), Hence, design seismic force, for the equipment Weight of the equipment, Wp = 100 kN IITK-GSDMA-EQ21-V2.0 0.24 ⎛ 16.2 ⎞ 1.0 (1)(100 ) kN ⎜1 + ⎟ 2 ⎝ 16.2 ⎠ 2.5 Fp =10.0 kN. Example 7/Page 16 Examples on IS 1893(Part 1) The anchorage of equipment with the building must be designed for twice of this force (Clause 7.13.3.4 of draft IS 1893) Shear per anchor bolt, V = 2Fp/4 =2 × 10.0/4 kN =5.0 kN The overturning moment is M ot = 2.0 × (10.0 kN) × (1.5 m) = 30.0 kN-m The overturning moment is resisted by two anchor bolts on either side. Hence, tension per anchor bolt from overturning is Ft = (30.0) kN (1.0)(2) =15.0kN IITK-GSDMA-EQ21-V2.0 Example 7/Page 17 Examples on IS 1893(Part 1) Example 8 – Anchorage Design for an Equipment Supported on Vibration Isolator Problem Statement: A 100 kN electrical generator of a emergency power supply system is to be installed on the fourth floor of a 6-storey hospital building in Guwahati (zone V). It is to be mounted on four flexible vibration isolators, one at each corner of the unit, to damp the vibrations generated during the operation. Floor to floor height of the building is 3.0 m. except the ground storey which is 4.2 m. Determine the shear and tension demands on the isolators during earthquake shaking. Wp Fp Vibration CG 0 .8 m Isolator 1.2 m Figure 8.1 – Electrical generator installed on the floor Solution: Zone factor, Z = 0.36 (for zone V, Table 2 of IS 1893), Height of point of attachment of the generator above the foundation of the building, x = (4.2 + 3.0 × 3) m = 13.2 m, Height of the building, h = (4.2 + 3.0 × 5) m Amplification factor of the generator, a p = 2.5 (flexible component, Table 11), Response modification factor Rp = 2.5 (vibration isolator, Table 11), Importance factor Ip = 1.5 (life safety component, Table 12), Weight of the generator, Wp = 100 kN The design lateral force on the generator, Fp = Z ⎛ x ⎞ ap I pW p ⎜1 + ⎟ 2 ⎝ h ⎠ Rp = 19.2 m, IITK-GSDMA-EQ21-V2.0 Example 8/Page 18 Examples on IS 1893(Part 1) = 0.36 ⎛ 13.2 ⎞ 2.5 (1.5)(100 ) kN ⎜1 + ⎟ 2 ⎝ 19.2 ⎠ 2.5 = 45.6 kN 0.1Wp = 10.0kN Since the generator is mounted on flexible vibration isolator, the design force is doubled i.e., Fp = 2 × 45.6 kN = 91.2 kN Shear force resisted by each isolator, V = Fp/4 = 22.8 kN The overturning moment, M ot = ( 91.2 kN ) × ( 0.8 m ) = 73.0 kN-m The overturning moment (Mot) is resisted by two vibration isolators on either side. Therefore, tension or compression on each isolator, Ft = ( 73.0 ) kN (1.2 )( 2 ) = 30.4 kN IITK-GSDMA-EQ21-V2.0 Example 8/Page 19 Examples on IS 1893(Part 1) Example 9 – Design of a Large Sign Board on a Building Problem Statement: A neon sign board is attached to a 5-storey building in Ahmedabad (seismic zone III). It is attached by two anchors at a height 12.0 m and 8.0 m. From the elastic analysis under design seismic load, it is found that the deflections of upper and lower attachments of the sign board are 35.0 mm and 25.0 mm, respectively. Find the design relative displacement. Solution: Since sign board is a displacement sensitive nonstructural element, it should be designed for seismic relative displacement. Height of level x to which upper connection point is attached, hx = 12.0 m Height of level y to which lower connection point is attached, hy = 8.0 m Deflection at building level x of structure A due to design seismic load determined by elastic analysis = 35.0 mm Deflection at building level y of structure A due to design seismic load determined by elastic analysis = 25.0 mm Response reduction factor of the building R = 5 (special RC moment resisting frame, Table 7) δ xA = 5 x 35 = 175.0 mm δ yA = 5 x 25 = 125.0 mm IITK-GSDMA-EQ21-V2.0 (i) D p = δ xA − δ yA = (175.0 – 125.0) mm = 50.0 mm Design the connections of neon board to accommodate a relative motion of 50 mm. (ii) Alternatively, assuming that the analysis of building is not possible to assess deflections under seismic loads, one may use the drift limits (this presumes that the building complies with seismic code). Maximum interstorey drift allowance as per clause 7.11.1 is IS : 1893 is 0.004 times the storey height, i.e., Δ aA = 0.004 hsx D p = R (hx − h y ) Δ aA hsx =5 (12000.0 – 8000.0)(0.004) mm = 80.0 mm The neon board will be designed to accommodate a relative motion of 80 mm. Example 9/Page 20 Examples on IS 1893(Part 1) Example: 10 Liquefaction Analysis using SPT data Problem Statement: The measured SPT resistance and results of sieve analysis for a site in Zone IV are indicated in Table 10.1. The water table is at 6m below ground level. Determine the extent to which liquefaction is expected for 7.5 magnitude earthquake. Estimate the liquefaction potential and resulting settlement expected at this location. Table 10.1: Result of the Standard penetration Test and Sieve Analysis Depth (m) 0.75 N 60 Soil Classification Percentage fine 11 9 Poorly Graded Sand and Silty Sand (SP-SM) 3.75 17 Poorly Graded Sand and Silty Sand (SP-SM) 16 6.75 13 Poorly Graded Sand and Silty Sand (SP-SM) 12 9.75 18 Poorly Graded Sand and Silty Sand (SP-SM) 8 12.75 17 Poorly Graded Sand and Silty Sand (SP-SM) 8 15.75 15 Poorly Graded Sand and Silty Sand (SP-SM) 7 18.75 26 Poorly Graded Sand and Silty Sand (SP-SM) 6 Solution: evaluated = 12.75m Site Characterization: This site consists of loose to dense poorly graded sand to silty sand (SP-SM). The SPT values ranges from 9 to 26. The site is located in zone IV. The peak horizontal ground acceleration value for the site will be taken as 0.24g corresponding to zone factor Z = 0.24 Initial stresses: Liquefaction Potential of Underlying Soil Step by step calculation for the depth of 12.75m is given below. Detailed calculations for all the depths are given in Table 10.2. This table provides the factor of safety against liquefaction (FSliq), maximum depth of liquefaction below the ground surface, and the vertical settlement of the soil due to liquefaction (Δv). σ v = 12.75 × 18.5 = 235.9 kPa u 0 = (12.75 − 6.00) × 9.8 = 66.2 kPa σ v' = (σ v − u 0 ) = 235.9 − 66.2 = 169.7 kPa Stress reduction factor: rd = 1 − 0.015 z = 1 − 0.015 × 12.75 = 0.81 Critical stress ratio induced by earthquake: a max = 0.24 g , M w = 7.5 ( CSReq = 0.65 × (a maz / g ) × rd × σ v / σ v' CSReq = 0.65 × (0.24) × 0.81 × (235.9 / 169.7 ) = 0.18 a max = 0.24 , M w = 7.5 , g γ sat = 18.5 kN / m 3 , γ w = 9.8 kN / m 3 Correction for SPT overburden pressure: Depth of water level below G.L. = 6.00m (N )60 Depth at which liquefaction potential is to be C N = 9.79 1 / σ v' IITK-GSDMA-EQ21-V2.0 ) (N) value for = C N × N 60 ( ) 1/ 2 Example 10/Page 21 Examples on IS 1893(Part 1) Figure F-22 (for SPT data) Figure F-22 (for CPT data: in “factor of safety” calculation in column 2 of page 24 this figure is wrongly cited as F-6) F 2.24 2.56 Figure F-4 provides a plot for km . Algebraically, the relationship is simply km =10 10 Mw subjected to km ≥ 0.75 Figure F-6 Figure F-5 F Figure F-8 IITK-GSDMA-EQ21-V2.0 Example 10/Page 21 A Examples on IS 1893(Part 1) C N = 9.79 (1 / 169.7 ) 1/ 2 CSR L = 0.14 × 1 × 1 × 0.88 = 0.12 = 0.75 (N )60 = 0.75 × 17 = 13 Factor of safety against liquefaction: FS L = CSR L / CSReq = 0.12 / 0.18 = 0.67 Critical stress ratio resisting liquefaction: Percentage volumetric strain (%ε) For ( N )60 = 13 , fines content of 8% For CSReql = CSReq / (k m kα kσ ) CSR7.5 = 0.14 (Figure F-2) = 0.18 / (1x1x0.88) = 0.21 Corrected Critical Stress Ratio Resisting Liquefaction: CSRL = CSR7.5 k m kα kσ (N 1 )60 = 13 %ε = 2.10 (from Figure F-8) Liquefaction induced vertical settlement (ΔV): k m = Correction factor for earthquake magnitude other than 7.5 (Figure F-4) (ΔV) = volumetric strain x thickness of liquefiable level = 1.00 for M w = 7.5 k α = Correction factor for initial driving static shear (Figure F-6) = 2.1 × 3.0 / 100 = 0.063m = 63mm Summary: Analysis shows that the strata between depths 6m and 19.5m are liable to liquefy. The maximum settlement of the soil due to liquefaction is estimated as 315mm (Table 10.2) = 1.00, since no initial static shear kσ = Correction factor for stress level larger than 96 kPa (Figure F-5) = 0.88 Table 10.2: Liquefaction Analysis: Water Level 6.00 m below GL (Units: Tons and Meters) σv σ v' Depth %Fine (kPa) (kPa) N 60 CN ( N )60 rd CSReq CSReql CSR7.5 CSR L FS L %ε ΔV 0.75 11.00 13.9 13.9 9.00 2.00 18 0.99 0.15 0.14 0.22 0.25 1.67 - - 3.75 16.00 69.4 69.4 17.00 1.18 20 0.94 0.15 0.14 0.32 0.34 2.27 - - 6.75 12.00 124.9 117.5 13.00 0.90 12 0.90 0.15 0.15 0.13 0.13 0.86 2.30 0.069 9.75 8.00 180.4 143.6 18.00 0.82 15 0.85 0.17 0.18 0.16 0.15 0.88 1.90 0.057 12.75 8.00 235.9 169.7 17.00 0.75 13 0.81 0.18 0.20 0.14 0.12 0.67 2.10 0.063 15.75 7.00 291.4 195.8 15.00 0.70 10 0.76 0.18 0.21 0.11 0.09 0.50 2.50 0.075 18.75 6.00 346.9 221.9 26.00 0.66 17 0.72 0.18 0.22 0.18 0.15 0.83 1.70 0.051 Total Δ IITK-GSDMA-EQ21-V2.0 0.315 Example 10/Page 22 Examples on IS 1893(Part 1) Example: 11 Liquefaction Analysis using CPT data Problem Statement: Prepare a plot of factors of safety against liquefaction versus depth. The results of the cone penetration test (CPT) of 20m thick layer in Zone V are indicated in Table 11.1. Assume the water table to be at a depth of 2.35 m, the unit weight of the soil to be 18 kN/m3 and the magnitude of 7.5. Table 11.1: Result of the Cone penetration Test Depth (m) qc fs 0.50 144.31 0.652 1.00 95.49 1.50 Depth (m) qc fs 7.50 45.46 0.132 0.602 8.00 39.39 39.28 0.281 8.50 2.00 20.62 0.219 2.50 150.93 3.00 Depth (m) qc fs 14.50 46.60 0.161 0.135 15.00 46.77 0.155 36.68 0.099 15.50 47.58 0.184 9.00 45.30 0.129 16.00 41.99 0.130 1.027 9.50 51.05 0.185 16.50 48.94 0.329 55.50 0.595 10.00 46.39 0.193 17.00 56.69 0.184 3.50 10.74 0.359 10.50 58.05 0.248 17.50 112.90 0.392 4.00 9.11 0.144 11.00 48.94 0.159 18.00 104.49 0.346 4.50 33.69 0.297 11.50 63.75 0.218 18.50 77.75 0.256 5.00 70.69 0.357 12.00 53.93 0.193 19.00 91.58 0.282 5.50 49.70 0.235 12.50 53.60 0.231 19.50 74.16 0.217 6.00 51.43 0.233 13.00 62.39 0.275 20.00 115.02 0.375 6.50 64.94 0.291 13.50 54.58 0.208 7.00 57.24 0.181 14.00 52.08 0.173 Solution: Liquefaction Potential of Underlying Soil Step by step calculation for the depth of 4.5m is given below. Detailed calculations are given in Table 11.2. This table provides the factor of safety against liquefaction (FSliq). The site is located in zone V. The peak horizontal ground acceleration value for the site will be taken as 0.36g corresponding to zone factor Z = 0.36 amax/g = 0.36, Mw=7.5, IITK-GSDMA-EQ21 –V2.0 γ sat = 18 kN / m 3 , γ w = 9.8 kN / m 3 Depth of water level below G.L. = 2.35m Depth at which liquefaction potential is to be evaluated = 4.5m Initial stresses: σ v = 4.5 × 18 = 81.00 kPa u 0 = (4.5 − 2.35) × 9.8 = 21.07 kPa σ v' = (σ v − u 0 ) = 81 − 21.07 = 59.93 kPa Stress reduction factor: Example 11 /Page 23 Examples on IS 1893(Part 1) Q = [(q c − σ v ) Pa ](Pa σ v′ ) rd = 1 − 0.000765 z = 1 − 0.000765 × 4.5 = 0.997 Critical stress earthquake: ratio induced ( CSReq = 0.65 × (a maz / g ) × rd × σ v / σ by ' v ) CSReq = 0.65 × (0.36) × 0.997 × (81 / 59.93) = 0.32 n Q = [(3369 − 81) 101.35] × (101.35 59.93) = 42.19 0.5 K c = −0.403(2.19 ) + 5.581(2.19 ) − 21.63(2.19 ) 4 M 3 2 + 33.75(2.19 ) − 17.88 = 1.64 Normalized Cone Tip Resistance: Corrected Critical Stress Ratio Resisting Liquefaction: CSRL = CSReq k m kα kσ (qc1N )cs = K c (Pa σ v′ ) (q c Pa ) n (q c1N )cs = 1.64(101.35 59.93)0.5 (3369 101.35) = 70.77 k m = Correction factor for earthquake magnitude other than 7.5 (Figure F-4) Factor of safety against liquefaction: For (q c1N )cs = 70.77 , = 1.00 for M w = 7.5 k α = Correction factor for initial driving static shear (Figure F-6) CRR =0.11 (Figure F-6) FS liq = CRR / CSR L FS liq = 0.11 / 0.32 = 0.34 = 1.00 , since no initial static shear kσ = Correction factor for stress level larger than 96 kPa (Figure F-5) = 1.00 CSR L = 0.32 × 1 × 1 × 1 = 0.32 Summary: Analysis shows that the strata between depths 0-1m are liable to liquefy under earthquake shaking corresponding to peak ground acceleration of 0.36g. The plot for depth verses factor of safety is shown in Figure 11.1 Correction factor for grain characteristics: K c = 1 .0 for I c ≤ 1.64 and 4 3 K c = −0.403I c + 5.581I c − 21.63I c + 33.75 I c − 17.88 M 2 for I c > 1.64 The soil behavior type index, I c , is given by Ic = (3.47 − log Q )2 + (1.22 + log F )2 Ic = (3.47 − log 42.19)2 + (1.22 + log 0.903)2 = 2.19 Where, F = f (q c − σ v ) × 100 F = [29.7 / (3369 − 81)] × 100 = 0.903 and IITK-GSDMA-EQ21-V2.0 Example 11/Page 24 Examples on IS 1893(Part 1) Table 11.2: Liquefaction Analysis: Water Level 2.35 m below GL (Units: kN and Meters) Depth σv σv ' rd qc (kPa) fs (kPa) CSReq CSRL F Q Ic Kc (qc1N)cs CRR FSliq 0.50 9.00 9.00 1.00 14431 65.20 0.23 0.23 0.45 241.91 1.40 1.00 242.06 100.00 434.78 1.00 18.00 18.00 1.00 9549 60.20 0.23 0.23 0.63 159.87 1.63 1.00 160.17 100.00 434.78 1.50 27.00 27.00 1.00 3928 28.10 0.23 0.23 0.72 65.43 1.97 1.27 83.53 0.13 0.57 2.00 36.00 36.00 1.00 2062 21.90 0.23 0.23 1.08 33.54 2.31 1.99 68.04 0.11 0.47 2.50 45.00 43.53 1.00 15093 102.70 0.24 0.24 0.68 226.55 1.53 1.00 227.23 100.00 416.67 3.00 54.00 47.63 1.00 5550 59.50 0.26 0.26 1.08 79.10 2.01 1.31 105.02 0.19 0.73 3.50 63.00 51.73 1.00 1074 35.90 0.28 0.28 3.55 13.96 2.92 5.92 87.81 0.14 0.50 4.00 72.00 55.83 1.00 911 14.40 0.30 0.30 1.72 11.15 2.83 5.01 60.64 0.10 0.33 4.50 81.00 59.93 1.00 3369 29.70 0.32 0.32 0.90 42.19 2.19 1.64 70.77 0.11 0.34 5.00 90.00 64.03 1.00 7069 35.70 0.33 0.33 0.51 86.63 1.79 1.10 96.60 0.16 0.48 5.50 99.00 68.13 1.00 4970 23.50 0.34 0.34 0.48 58.62 1.93 1.22 72.68 0.12 0.35 6.00 108.00 72.23 1.00 5143 23.30 0.35 0.35 0.46 58.85 1.92 1.21 72.45 0.12 0.34 6.50 117.00 76.33 1.00 6494 29.10 0.36 0.36 0.46 72.50 1.83 1.13 83.61 0.13 0.36 7.00 126.00 80.43 0.99 5724 18.10 0.36 0.36 0.32 62.00 1.83 1.13 71.56 0.11 0.31 7.50 135.00 84.53 0.99 4546 13.20 0.37 0.37 0.30 47.66 1.92 1.21 59.46 0.10 0.27 8.00 144.00 88.63 0.99 3939 13.50 0.38 0.38 0.36 40.04 2.02 1.33 55.18 0.10 0.26 8.50 153.00 92.73 0.99 3668 9.90 0.38 0.38 0.28 36.26 2.02 1.33 50.45 0.09 0.24 9.00 162.00 96.83 0.99 4530 12.90 0.39 0.39 0.30 44.09 1.95 1.24 56.79 0.10 0.26 9.50 171.00 100.93 0.75 5105 18.50 0.30 0.30 0.37 48.78 1.95 1.24 62.62 0.10 0.33 10.00 180.00 105.03 0.73 4639 19.30 0.29 0.29 0.43 43.22 2.02 1.33 59.94 0.10 0.34 10.50 189.00 109.13 0.72 5805 24.80 0.29 0.29 0.44 53.40 1.95 1.23 68.16 0.11 0.38 11.00 198.00 113.23 0.71 4894 15.90 0.29 0.29 0.34 43.84 1.98 1.27 58.01 0.10 0.34 11.50 207.00 117.33 0.69 6375 21.80 0.29 0.29 0.35 56.56 1.88 1.17 68.51 0.11 0.38 12.00 216.00 121.43 0.68 5393 19.30 0.28 0.28 0.37 46.67 1.97 1.26 61.23 0.10 0.36 12.50 225.00 125.53 0.67 5360 23.10 0.28 0.28 0.45 45.53 2.01 1.31 62.48 0.10 0.36 13.00 234.00 129.63 0.65 6239 27.50 0.28 0.28 0.46 52.39 1.96 1.25 68.09 0.11 0.39 13.50 243.00 133.73 0.64 5458 20.80 0.27 0.27 0.40 44.79 2.00 1.29 60.67 0.10 0.37 14.00 252.00 137.83 0.63 5208 17.30 0.27 0.27 0.35 41.93 2.00 1.30 57.21 0.10 0.37 14.50 261.00 141.93 0.61 4660 16.10 0.26 0.26 0.37 36.68 2.06 1.39 53.90 0.09 0.35 15.00 270.00 146.03 0.60 4677 15.50 0.26 0.26 0.35 36.23 2.06 1.38 53.24 0.09 0.35 15.50 279.00 150.13 0.59 4758 18.40 0.25 0.25 0.41 36.31 2.08 1.43 55.02 0.10 0.40 16.00 288.00 154.23 0.57 4199 13.00 0.25 0.25 0.33 31.28 2.11 1.47 49.44 0.09 0.36 16.50 297.00 158.33 0.56 4894 32.90 0.25 0.25 0.72 36.29 2.19 1.65 63.63 0.10 0.40 17.00 306.00 162.43 0.55 5669 18.40 0.24 0.24 0.34 41.80 2.00 1.30 57.28 0.10 0.42 17.50 315.00 166.53 0.53 11290 39.20 0.24 0.24 0.36 84.48 1.73 1.06 91.71 0.15 0.63 18.00 324.00 170.63 0.52 10449 34.60 0.23 0.23 0.34 76.99 1.75 1.07 85.35 0.14 0.61 18.50 333.00 174.73 0.51 7775 25.60 0.23 0.23 0.34 55.92 1.88 1.17 68.46 0.11 0.48 19.00 342.00 178.83 0.49 9158 28.20 0.22 0.22 0.32 65.48 1.81 1.11 75.57 0.12 0.55 19.50 351.00 182.93 0.48 7416 21.70 0.22 0.22 0.31 51.89 1.89 1.18 64.35 0.10 0.45 20.00 360.00 187.03 0.47 11502 37.50 0.21 0.21 0.34 80.93 1.73 1.06 88.47 0.14 0.67 IITK-GSDMA-EQ21-V2.0 Example 11/Page 25 Examples on IS 1893(Part 1) Factor of Safety 0.0 0.5 1.0 1.5 2.0 0 3 5 Depth (m) 8 10 13 15 18 20 Figure 11.1: Factor of Safety against Liquefaction IITK-GSDMA-EQ21-V2.0 Example 11/Page 26

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